Lagrangian formulations of self-dual gauge theories in diverse dimensions

Abstract

In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral n-form gauge theories, for n = 2 p in D = 4 p + 2 dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG model, we generalize the earlier Lagrangian formulation based on a decomposition of spacetime into ( D − 1 ) dimensions plus a special dimension, to construct Lagrangian formulations based on a generic decomposition of spacetime into D ′ and D ″ = D − D ′ dimensions. Although the Lorentz symmetry is not manifest, we prove that the action is invariant under modified Lorentz transformations.